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Proof step 18 from proof pot-square-est-01 (previous step)

i1 * i1 * 4 < (i1 + 1) * (i1 + 1), i1 * i1 < 4 ^ i1, i1 * i1 * 4 < 4 ^ i1 * 4, 0 ≤ i1, 4 ^ i1 * 4 ≤ (i1 + 1) * (i1 + 1), ∀ i0. i→n(i0) < i→n(i1 + 1) → 4 ^ i0 ≤ i0 * i0 ∧ 0 ≤ i0 → false ⊦ (i1 + 1) * (i1 + 1) = i1 * i1 + 2 * i1 + 1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult name: dist-lsplit seq: ⊦ (i + i0) * j = i * j + i0 * j subst: [j, i0, i] → [i1 + 1, 1, i1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ 1 * i = i; (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ i * j + i = i * (j + 1); (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ i * j + i * j0 = i * (j + j0); (s)% ⊦ i + j = i + i0 ↔ j = i0; (s) Used terms: i1 + 1, 1, i1